Complete Solutions to the Rate Equations Describing Q-Spoiled and PTM Laser Operation

Abstract

The solutions of the rate equations describing the Q-spoiled and pulsed-transmission-mode (PTM) operation of a three-level laser are given. These solutions were carried out in two time regions: (1) the delay time followed by (2) the pulse time. Region (1) was tractable with approximate analytic methods, while in region (2) the equations were solved by analog computer. The effect of the duration of the Q switch on the delay time and on the PTM operation is investigated. It is found that Q-switch times as long as 20 nsec give satisfactory PTM operation.

Regenerative Amplification of Femtosecond Pulses: Design andConstruction of a sub-100fs, muon J Laser System

“…The theoretical treatment of Q-switching was presented in 1965 [40]and has remained essentially unchanged. It is based on a solution of the two rate equations, which describe the changes in population difference per volume .6.N(t) and photon density n(t) in the laser.…”

The Linear Theory of Landau Damping

“…This usually means that the switching time has to be less than two resonator loop transit times. Under these conditions the loop gain is constant during the formation time, and so the number of loop transits p required for the resonator photon density to increase from its initial value 4i to +A is given by (McClung andHellwarth 1963, Kay andWaldman 1965) Here exp (201iZ) is the loop gain of a ruby of length I, 1 -e-r is the resonator loop loss, and at threshold 2ail = y. Since the factor In ($a/+i) is insensitive to variations in ai (Kay and Waldman 1965), 201iZ -y should be proportional to p-1.…”

Theoretical and experimental study of a laser-diode-pumped actively Q-switched Nd:YVO4 laser with acoustic–optic modulator

“…Since the equations describing the performance of rapidly Q-switched lasers were first derived about four decades ago [5,6], the rate equations obtained under the plane-wave approximation for LDpumped Q-switched lasers have still been used [3,4,7]. The plane-wave approximation assumes that the population-inversion density and the intracavity photon density within the beam cross section only depend on time [7,8].…”